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Theorem pm2.68dc 793
Description: Concluding disjunction from implication for a decidable proposition. Based on theorem *2.68 of [WhiteheadRussell] p. 108. Converse of pm2.62 667 and one half of dfor2dc 794. (Contributed by Jim Kingdon, 27-Mar-2018.)
Assertion
Ref Expression
pm2.68dc  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )

Proof of Theorem pm2.68dc
StepHypRef Expression
1 jarl 584 . 2  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( -.  ph  ->  ps ) )
2 pm2.54dc 790 . 2  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2syl5 28 1  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 629  DECID wdc 742
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-dc 743
This theorem is referenced by:  dfor2dc  794
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